Julian Otalvaro

We present a framework for maximum likelihood analysis on count observations that begin high and quickly drop to zero, for example, from hollow fiber drug comparison studies. This simulation study focuses on treating observed counts as Poisson or normally distributed for the purpose of estimating infection rebound after effective treatment. CFU profiles were simulated from inoculation to 96 h post‐treatment. The PK‐PD link was an Emax inhibitory model. Random parameters were pathogen growth and natural decay rates, drug concentration for half‐maximal effect, and drug pathogen kill rate. Other parameters, including PK, were fixed. Parameters were adjusted to attain 67% efficacy at 24 h. Random parameter values were optimized for profiles observed at 24, 48, 72, and 96 h assuming each of four probability assumptions: (1) all CFU measurements were Poisson distributed (truth); (2) CFU < 128 were Poisson, higher values were normally distributed; (3) all observations were normally distributed; and (4) observations were normally distributed but CFU < 10 were censored. CFU‐time profiles were re‐simulated using the optimized parameter densities. Rebound percentage (CFU ≥ 10 at 24 h post‐treatment) was best predicted using strategy 2, above. For limited periodically collected time series count data that quickly fall to 0, the true proportion reaching 0 (lack of rebound) was best modeled by assuming Poisson distribution at low counts. At higher counts (≥ 128), assuming normality is reasonable. Censoring observations leads to biased models.

To establish bioequivalence (BE) of a generic test formulation with respect to a reference listed drug, it is necessary to demonstrate a comparable rate and extent to which active ingredients reach the site of action. To decrease unnecessary human testing and simulate scenarios involving specific populations or challenges with recruitment or study design, industry and regulators are increasingly considering in silico virtual bioequivalence (VBE) approaches. This tutorial introduces the VBEToolbox R package: a toolbox within the Open Systems Pharmacology framework to streamline and standardize computational VBE workflows. The package integrates in vitro and in vivo data to train pharmacokinetic models through inference of inter‐individual variability from clinical data and establishment of in vitro to in vivo extrapolations. A nonparametric approach is adopted to account for uncertainties from parameter non‐identifiability. The trained model is then applied to determine the study size with statistical power needed to demonstrate BE virtually. The use of the VBE tool is illustrated with two case studies. The first evaluates the VBE of petrolatum and ethylene glycol dermal formulations of testosterone by integrating in vitro skin permeation tests, vehicle/skin partitioning data, testosterone solubility data, and in vivo absorption data in a mechanistic in vitro/in vivo dermal absorption model. The second assesses the VBE of two oral bupropion formulations by integrating in vitro dissolution data in a physiologically based pharmacokinetic model. These case studies highlight essential considerations for model development, training, and extrapolation toward application for VBE assessment.

This paper introduces a non-parametric estimation algorithm designed to effectively estimate the joint distribution of model parameters with application to population pharmacokinetics. Our research group has previously developed the non-parametric adaptive grid (NPAG) algorithm, which while accurate, explores parameter space using an ad-hoc method to suggest new support points. In contrast, the non-parametric optimal design (NPOD) algorithm uses a gradient approach to suggest new support points, which reduces the amount of time spent evaluating non-relevant points and by this the overall number of cycles required to reach convergence. In this paper, we demonstrate that the NPOD algorithm achieves similar solutions to NPAG across two datasets, while being significantly more efficient in both the number of cycles required and overall runtime. Given the importance of developing robust and efficient algorithms for determining drug doses quickly in pharmacokinetics, the NPOD algorithm represents a valuable advancement in non-parametric modeling. Further analysis is needed to determine which algorithm performs better under specific conditions.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis–Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi‐Random Parametric Expectation Maximization (QRPEM) for a realistic two‐compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log‐normal cases.

In this paper we describe NPSA, the first parallel nonparametric global maximum likelihood optimization algorithm using simulated annealing (SA). Unlike the nonparametric adaptive grid search method NPAG, which is not guaranteed to find a global optimum solution, and may suffer from the curse of dimensionality, NPSA is a global optimizer and it is free from these grid related issues. We illustrate NPSA by a number of examples including a pharmacokinetics (PK) model for Voriconazole and show that NPSA may be taken as an upgrade to the current grid search based nonparametric methods.

Inspired from quantum Monte Carlo, by using unbiased estimators all the time and sampling discrete and continuous variables at the same time using Metropolis algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). In particular, we compared RPEM with Monolix's SAEM and Certara's QRPEM for a realistic two-compartment Voriconazole model with ordinary differential equations (ODEs) and using simulated data. We show that RPEM is 3 to 4 times faster than SAEM and QRPEM, and more accurate than them in reconstructing the population parameters.

The combination of ampicillin (AMP) and ceftriaxone (CRO) is considered synergistic againstEnterococcus faecalisbased onin vitrotests and the rabbit endocarditis model, however,in vitroassays are limited by the use of fixed antibiotic concentrations and the rabbit model by poor bacterial growth, high variability, and the use of point dose-effect estimations, that may lead to inaccurate assessment of antibiotic combinations and hinder optimal translation. Here, we tested AMP+CRO against two strains ofE.faecalisand one ofE.faeciumin an optimized mouse thigh infection model that yields high bacterial growth and allows to define the complete dose-response relationship. By fitting Hill’s sigmoid model and estimating the parameters maximal effect (E_max) and effective dose 50 (ED₅₀), the following interactions were defined: synergism (E_maxincrease ≥2 log₁₀CFU/g), antagonism (E_maxreduction ≥1 log₁₀CFU/g) and potentiation (ED₅₀reduction ≥50% without changes in E_max). AMP monotherapy was effective against the three strains, yielding valid dose-response curves in terms of dose and the indexfT_>MIC. CRO monotherapy showed no effect. The combination AMP+CRO againstE.faecalisled to potentiation (59–81% ED₅₀reduction) and not synergism (no changes in E_max). AgainstE.faecium, the combination was indifferent. The optimized mouse infection model allowed to obtain the complete dose-response curve of AMP+CRO and to define its interaction based on pharmacodynamic parameter changes. Integrating these results with the pharmacokinetics will allow to derive the PK/PD index bound to the activity of the combination, essential for proper translation to the clinic.